-M 
•soia 


The  Hydration  of  Normal  Sodium  Pyrophosphate 

to  Orthophosphate  in  Varying  Concentrations 

of  Hydrogen  Ion  at  Forty-five  Degrees 

Centigrade. 


DISSERTATION 

Submitted  in  Partial  Fulfillment  of  the  requirements 

for  the  Degree  of  Doctor  of  Philosophy  in 

the  Faculty  of  Pure  Science  of 

Columbia  University. 


BY 

WALDEMAR  C.  HANSEN,  B.  S. 

NEW  YORK  CITY 
1922 


The  Hydration  of  Normal  Sodium  Pyrophosphate 

to  Orthophosphate  in  Varying  Concentrations 

of  Hydrogen  Ion  at  Forty-five  Degrees 

Centigrade. 


DISSERTATION 

Submitted  in  Partial  Fulfillment  of  the  requirements 

for  the  Degree  of  Doctor  of  Philosophy  in 

the  Faculty  of  Pure  Science  of 

Columbia  University. 


BY 

WALDEMAR  C.  HANSEN,  B.  S. 

NEW  YORK  CITY 
1922 


TO  MY  MOTHER 


ACKNOWLEDGMENT 

The  following  investigation  was  undertaken  at 
the  suggestion  of  Professor  Samuel  J.  Kiehl  and  car- 
ried out  under  his  direction.  It  gives  me  pleasure  to 
express  my  thanks  and  appreciation  for  his  constant 
advice  and  assistance  received  throughout  the  inves- 
tigation. 


A87139 


The  Hydration  of  Normal  Sodium  Pyrophosphate  to  Ortho- 
phosphate  in  Varying  Concentrations  of  Hydrogen 
Ion  at  45°  Centigrade. 

Since  the  work  of  Graham1  on  the  phosphoric  acids  the 
problem  of  the  hydration  of  pyrophosphoric  acid  has  been  of 
interest.  A  part  of  the  interest  was  due  to  the  difference  of 
opinion  among  chemists  as  to  whether  the  hydration  of  meta- 
phosphoric  acid  was  direct  to  orthophosphoric  acid  or 
whether  pyrophosphoric  acid  was  formed  as  an  intermediate 
product1'  2>  3>  4>  5»  6>  7.  Beans  and  Kiehl8  showed  that  pyro- 
phosphate  is  formed  as  an  intermediate  product  in  the  hydra- 
tion of  sodium  monometaphosphate  to  orthophosphate.  There- 
fore to  understand  more  fully  the  hydration  of  sodium  mono- 
metaphosphate to  orthophosphate  it  seems  advisable  to  study 
the  hydration  of  a  pyrophosphate  to  orthophosphate  under 
the  same  conditions. 

One  difficulty  encountered  by  previous  workers  on  this 
problem  was  due  to  the  lack  of  a  suitable  method  for  the  de- 
termination of  the  amounts  of  the  different  phosphates  pres- 
ent when  present  together.  In  order  to  study  the  reaction  it 
is  necessary  to  have  a  method  of  determining  the  amounts  of 
each  of  the  phosphates  present  at  any  given  time. 

The  first  to  study  this  problem  were  Andre  and  Berthelot5. 
They  used  a  method  of  acidimetry  to  determine  the  amounts  of 
each  of  the  acids  present  at  any  definite  time.  They  discarded 
this  method  and  attempted5  to  develop  a  gravimetric  separa- 
tion. In  this  separation  they  precipitated  a  magnesium  ammon- 
ium pyrophosphate  of  indefinite  composition  by  heating  the 
solution  to  be  analyzed,  acidified  with  acetic  acid,  for  three  or 
four  hours  on  a  boiling  water  bath.  Since  temperature9  and 
hydrogen  ion  5>  9  both  have  a  marked  effect  on  the  rate  of 
hydration  this  method  could  not  be  applicable  for  a  quantita- 
tive study  of  this  hydration. 

No  one  attempted  a  further  study  of -this  problem  until 
1909  when  Abbott9  studied  it  by  conductivity  measurements. 
In  his  method  he  measured  the  conductivity  of  aqueous  solu- 


tions  of  pyrophosphoric  acid  of  varying  concentrations  and 
at  different  temperatures.  The  time  at  which  the  conduc- 
tivity of  a  given  solution  became  constant  he  considered  as 
the  time  required  for  the  complete  hydration.  He  determined 
the  amounts  hydrated  at  different  intervals  during  the  reaction 
by  measuring  the  conductivity  of  mixtures  of  pyrophosphoric 
acid  and  orthophosphoric  acid  corresponding  in  composition 
to  certain  percentages  of  hydration  of  an  original  pyrophos- 
phoric acid  solution.  He  plotted  these  conductivity  values 
against  composition  and  got  straight  line  curves.  So  by  meas- 
uring the  conductivity  of  his  hydration  solution  and  referring 
to  the  curves  he  could  determine  the  percentage  hydrated  at 
that  time. 

These  three  studies  are  the  only  ones  which  have  been 
made  heretofore  in  which  the  reaction  has  been  followed 
throughout  its  entire  course.  Since  the  method5  of  Andre  and 
Berthelot  was  not  applicable  to  the  problem  in  question,  and 
since  Abbott's  investigations  were  at  temperatures  wrhere  the 
reaction  was  complete  in  a  few  hours  and  on  a  few  concen- 
trations of  pyrophosphoric  acid  only,  thus  limiting  the  con- 
centration of  hydrogen  ion  to  that  furnished  by  the  acid, 
neither  investigation  has  furnished  sufficient  information  re- 
garding the  hydration  of  a  pyrophosphate  as  compared  with 
the  hydration  of  a  metaphosphate  as  previously  pointed  out8. 
Therefore  this  problem  was  undertaken  to  study  the  hydration 
of  a  pyrophosphate  to  the  orthophosphate  in  varying  concen- 
trations of  hydrogen  ion  and  at  constant  temperature.  With 
this  in  view,  materials  have  been  prepared  and  methods  devel- 
oped whereby  the  factors  and  conditions  influencing  the  reac- 
tion could  be  controlled  and  studied  to  completion.  An  ac- 
count of  this  investigation  will  be  presented  under  the  follow- 
ing headings  Apparatus,  Preparation  of  Materials,  Method  of 
Procedure,  Experimental  Data,  Discussion,  and  Summary. 

APPARTUS 

Thermostat:  A  Freas  sensitive  thermostat  was  used  to 
maintain  a  constant  temperature  for  the  entire  work  of  hydra- 
tion and  hydrogen  ion  concentration  measurement.  By  it  a 
constant  temperature  of  45°  C.  ±  .01  was  secured. 

8 


Potentiometer :  Measurements  for  the  determination  of 
the  concentration  of  hydrogen  ion  were  made  with  a  Leeds 
and  Northrup  direct-reading  potentiometer  of  low  resistance. 

Galvanometer:  In  connection  with  the  potentiometer  a 
Leeds  and  Northrup,  type  R,  D'Arsonval  galvanometer  equip- 
ped with  a  telescope  and  scale  was  employed.  Its  resistance 
was  510  ohms,  its  sensibility  309  megohms.  The  period  was 
2.7  seconds,  and  the  critical  damping  resistance  was  1800 
ohms. 

Standard  Cell:  A  model  4,  No.  4208  Weston  standard  cell 
served  as  a  basis  for  all  electrical  measurements.  Its  value 
was  1.01872  volts  at  22°  C.  This  voltage  was  checked  against 
a  cell  whose  value  was  checked  against  a  Bureau  of  Standards 
standard. 

Calomel  and  Hydrogen  Cells  and  Electrodes :  The  calomel 
and  hydrogen  cells  and  electrodes  employed  in  the  measure- 
ment of  hydrogen  ion  concentration  w|ere  of  the  type  described 
in  the  article  of  Fales  and  Vosburgh10  excepting  a  modifica- 
tion of  the  hydrogen  cell  by  a  stop  cock  on  the  arm  leading  to 
the  salt  bridge. 

Crucible  Furnace :  The  amount  of  water  of  hydration  and 
of  constitution  of  the  di-sodium  orthophosphate  and  the 
amount  of  water  of  hydration  of  the  normal  sodium  pyro- 
phosphate  was  determined  by  heating  the  salts  in  an  electric 
resistance  furnace.  It  was  calibrated  for  temperature  by  a 
thermocouple  in  such  a  way  that  its  temperature  could  be  con- 
trolled by  measurement  of  the  current  with  an  accuracy  of 
±  10°  C. 

PREPARATION  OF  MATERIALS 

Normal  Sodium  Pyrophosphate  (Na4P2O7-10H2O) :  The 
purest  Normal  Sodium  Pyrophosphate  obtainable  was  re- 
crystallized  three  times  from  distilled  water.  The  solution  of 
the  pyrophosphate  was  cooled  in  ice  water  and  stirred  con- 
tinuously until  the  crystallization  was  complete;  this  gave  a 
very  uniform  crystalline  product.  The  crystals  were  washed 
three  times  with  distilled  water  on  a  Buchner  funnel  with  sue- 


tion.  They  were  then  spread  out  on  a  glass  surface  and  al- 
lowed to  dry  for  about  twelve  hours  at  room  temperature. 
They  were  then  finely  pulverized  in  an  agate  mortar  and 
stored  in  a  glass-stoppered  bottle. 

This  normal  sodium  pyrophosphate  was  analyzed  for  water 
of  hydration  by  weighing  a  sample  into  a  platinum  crucible 
and  heating  in  the  electric  crucible  furnace  previously  de- 
scribed. The  temperature  was  gradually  raised  to  450°  C. 
during  the  first  hour  by  increasing  the  current.  It  was  kept 
at  that  temperature  for  two  hours  and  then  weighed ;  reheat- 
ing for  an  hour  caused  no  change  in  weight.  The  following 
table  gives  the  analysis  of  the  normal  sodium  pyrophosphate 
used  in  this  research : 


Lot  I, 

Sample  1 
Sample  2 
Sample  3 
Lot  II, 

Sample  1 
Sampel  2 


Water  of  Hydration  Average 

40.45% 

40.44%  40.45% 

40.46% 


40.45% 


40.45% 
40.45% 

The  theoretical    value    for   water   of    hydration  of  Na4P2O7- 
10H2O  is  40.36%. 

It  was  then  analyzed  for  phosphorus  content.  The  phos- 
phorus content  was  calculated  on  the  basis  that  the  material 
was  Na4P2O7-XH2O  where  XH2O  =  40.45%.  The  percentage 
of  phosphorus  as  calculated  should  be  13.89%.  This  was 
checked  by  converting  weighed  samples  to  orthophosphate  by 
boiling  with  six  molar  hydrochloric  acid  for  from  four  to  five 
hours.  The  orthophosphate  was  then  determined  by  the 
standard  magnesium  mixture  method.  The  following  table 
gives  the  results  of  these  analyses : 

Lot  I. 


Na 


Sample 
1.... 
2.... 
3.... 
4.. 


L4P2O7-XH2O 

P  calc.  on 

P  determined 

Taken 

basis  of  13.89% 

as  ortho. 

.3269  gms. 

.0454  gms. 

.0458 

.4084 

.0568 

.0568 

.3971 

.0552 

.0556 

.4448 

.0618 

.0622 

10 


The  calculated  and  determined  values  for  percentage  of  phos- 
phorus in  the  material  check  within  experimental  error  and 
therefore  the  value  of  13.89  per  cent,  phosphorus  was  used  in 
making  up  all  solutions  for  hydrations. 

Di-Sodium  Orthophosphate  (Na2HPO4T2H2O)  :  Di-Sod- 
ium  orthophosphate  was  prepared  by  crystallizing  three  times 
from  distilled  water  by  the  addition  of  an  equal  volume  of  re- 
distilled 9Sr/<  alcohol  and  cooling  in  ice  water.  The  solution 
was  stirred  constantly  until  the  crystallization  was  complete. 
In  this  way  a  very  uniform  crystalline  product  was  secured. 
Di-sodium  orthophosphate  is  similar  to  mono-sodium  ortho- 
phosphate8  forming  two  liquid  phases  upon  the  addition  of 
the  alcohol,  and  crystallization  taking  place  first  at  the  junc- 
ture of  the  two  liquid  phases.  As  crystallization  proceeds  the 
upper  phase  disappears,  leaving  but  one  phase  at  complete 
precipitation.  The  crystals  were  filtered  on  a  Buchner  funnel 
with  suction  and  washed  three  times  with  alcohol.  They  were 
dried  by  spreading  out  on  a  glass  surface  for  about  an  hour  at 
room  temperature ;  at  the  end  of  that  time  they  were  finely 
pulverized  in  an  agate  mortar  and  put  in  a  glass-stoppered 
bottle.  Di-sodium  orthophosphate  crystallizes  as  Na2HPO4- 
12H2O  which  gradually  decomposes  forming  lower  hydrates 
when  exposed  to  the  air.  It  was,  therefore,  decided  not  to 
attempt  to  prepare  a  constant  hydrate,  but  to  dry  sufficiently 
to  remove  all  possibility  of  free  moisture  and  then  analyze 
that  material  for  water  of  constitution  and  water  of  hydration. 
The  analyses  for  water  content  were  made  by  weighing  a  sam- 
ple of  the  material  into  a  platinum  crucible  and  heating  in  the 
electric  furnace  previously  described  until  constant  weight 
was  obtained.  The  material  was  heated  gradually  for  one 
hour  at  first,  then  the  rheostat  was  set  for  a  temperature  of 
450°  C.  and  held  there  for  two  hours.  In  this  way  constant 
results  were  obtained  by  Na2HPO4-XH2O  being  converted  to 
Na4P2O7  and  the  loss  of  weight  was  the  total  water  content  of 
the  salt,  that  of  hydration  and  constitution. 


11 


Lot  I. 

%  water  of  constitu-  Calculated  %  of  phos- 

Sample             tion  and  hydration  Mean      phorus  in  the  material 

'  SIAS      iu2 


Lot  II. 

Sample 

1  ......  51  os  11  19 

2  ......  52.06 

Lot  III. 

Sample 

1  ......  56.51  r  ,  ri  _  1 

2  .....  .  56.52  5dSl  10'14 


Hydrochloric  Acid  :  The  hydrochloric  acid  used  was  pre- 
pared by  distilling  a  constant  boiling  solution  through  a 
quartz  condenser.  The  first  and  last  portions  were  rejected.  . 

Potassium  Chloride:  The  calomel  cells  and  salt  bridges 
were  prepared  from  potassium  chloride  which  was  purified  by 
re-crystallization  three  times  from  distilled  water  and  then 
fused  in  platinum. 

Mercurous  Chloride:  The  mercurous  chloride  employed  to 
make  calomel  cells  for  hydrogen  ion  concentration  measure- 
ments was  prepared  by  the  electrolytic  method  of  Ellis11,  from 
mercury  re-distilled  according  to  Hulett12  and  hydrochloric 
acid  prepared  as  described  above. 

Magnesium  Mixture:  The  magnesium  mixture  was  pre- 
pared by  dissolving  320  grams  of  magnesium  chloride  hexa 
hydrate,  225  grams  of  ammonium  chloride,  and  250  c.c.  of 
15  M.  ammonium  hydroxide  (specific  gravity  .9)  in  2250  c.c. 
of  water. 

Magnesium  Chloride  Solution:  The  magnesium  chloride 
solution  used  was  made  by  dissolving  110  grams  magnesium 
chloride  hexa  hydrate  in  50  c.c.  of  water,  which  gave  ap- 
proximately a  volume  of  130  c.c.  of  solution. 

12 


METHOD  OF  PROCEDURE 

In  planning  a  method  of  procedure  -the  first  considerations 
were  the  factors  influencing  the  reaction  and  they  have  as  far 
as  possible  been  either  measured  or  controlled  as  in  the  work 
of  Beans  and  Kiehl  in  the  hydration  of  sodium  monometa- 
phosphate.  The  temperature,  the  concentration  of  hydrogen 
ion,  the  concentration  of  orthophosphate  and  the  concentra- 
tion of  pyrophosphate  are  the  variable  factors  which  influence 
the  hydration  of  normal  sodium  pyrophosphate. 

The  temperature  was  regulated  and  controlled  at  45°  C. 
~  .01.  The  concentration  of  hydrogen  ion  was  measured  at 
intervals  during  the  hydration.  The  amount  of  pyrophos- 
phate changed  to  orthophosphate  was  determined  at  intervals 
by  hydrogen  ion  concentration  measurements ;  this  was  also 
checked  over  the  last  fifty  per  cent,  of  the  hydration  by  gravi- 
metric analysis. 

Preparation  of  Solutions: 

All  solutions  made  up  for  hydration  were  prepared  at  20° 
C.  The  finely  pulverized  normal  sodium  pyrophosphate  was 
weighed  and  transferred  to  a  1,000  c.c.  volumetric  flask.  Dis- 
tilled water  was  added  leaving  sufficient  room  for  the  hydro- 
. chloric  acid  required  to  furnish  the  hydrogen  ion  concentra- 
tion wanted  in  that  solution.  The  acid  used  was  the  constant 
boiling  mixture  previously  described.  The  value  of  the  acid 
was  determined  by  measuring  out  30  c.c.  portions  by  means  of 
a  burette  and  building  them  up  to  1,000  c.c.  at  20°  C.  These 
acid  solutions  were  titrated  with  standard  sodium  hydroxide 
solution.  The  value  of  the  sodium  hydroxide  solution  was 
determined  by  titration  against  Bureau  of  Standards  benzoic 
acid.  Phenolphthalein  was  used  as  indicator  in  all  the  titra- 
tion.s.  As  the  acid  was  added  the  flask  was  rotated  so  as  to 
avoid  acquiring  a  greater  hydrogen  ion  concentration  in  any 
portion  of  the  solution  than  that  ultimately  desired.  The  solu- 
tion was  then  brought  quickly  to  20°  C.,  and  the  flask  filled  to 
the  graduation,  then  mixed  thoroughly  and  put  in  a  "non  sol" 
bottle  and  placed  in  the  thermostat.  The  whole  operation  be- 
ginning with  the  addition  of  the  acid  required  not  more  than 
ten  minutes.  The  specific  gravity  of  the  solution  was  taken 

13 


at  20°  C.  by  means  of  the  Westphal  balance  calibrated  at 
20°  C.,  at  the  beginning  of  the  hydration,  again  at  about 
fifty  per  cent.,  and  finally  at  complete  hydration.  These  spe- 
cific gravity  values  are  given  in  the  tables  for  each  solution. 
There  Was  no  change  in  volume  in  any  of  the  solutions  during 
hydration  (except  D±  and  D2  see  Table  2)  greater  than  one 
part  in  a  thousand,  the  precision  of  the  balance.  This  was 
further  checked  by  measuring  the  specific  gravity  of  three  of 
the  solutions  at  the  beginning  and  at  the  end  of  the  reaction, 
by  means  of  a  pycnometer.  The  change  was  not  greater  than 
one  part  in  a  thousand  so  that  the  Westphal  balance  was  suffi- 
ciently accurate.  The  concentrations  of  all  of  the  solutions 
were  calculated  in  moles  per  liter  at  20°  C.  so  by  knowing  the 
specific  gravity  at  20°  C.  the  concentration  of  the  phosphates 
in  any  weighed  quantity  of  the  solution  could  be  calculated. 

The  change  of  specific  gravity  of  Dl  and  D.,  was  two  parts 
in  a  thousand.  Since  they  are  the  only  ones  that  show  this 
change  it  is  believed  to  be  due  to  some  other  cause  than  the 
change  in  volume  due  to  hydration.  The  final  hydrogen  ion 
concentrations  of  these  solutions  were  also  higher  than  expect- 
ed from  the  final  value  obtained  for  the  analytical  curve ;  all 
the  other  solutions  approached  quite  closely  in  final  hydrogen 
ion  concentrations  that  determined  for  the  analytical  curves. 
So  it  seems  quite  possible  that  some  evaporation  must  have 
taken  place  in  solutions  Dj  and  D2,  thus  making  them  more 
concentrated.  This  would  explain  both  the  specific  gravity 
change  and  the  higher  hydrogen  ion  concentration.  All  solu- 
tions were  handled  so  as  to  minimize  evaporation  as  much  as 
possible  because  at  45°  C.  and  for  the  long  times  that  the 
solutions  were  being  run  evaporation  would  become  quite 
appreciable  unless  every  precaution  was  taken  to  guard 
against  it. 

Measurement  of  Concentration  of  Hydrogen  Ion. 

All  hydrogen  ion  measurements  were  made  at  45°  C.  by 
The  Saturated  Potassium  Chloride  Calomel  Cell  method  de- 
veloped in  this  department13.  Samples  of  the  solution  in 
process  of  hydration  were  taken  by  means  of  a  pipette  and  in- 
troduced into  the  hydrogen  cell  previously  rinsed  three  times 

14 


with  the  solution  being  measured.  The  voltage  was  meas- 
ured after  ten  minutes  and  again  after  twenty  minutes  which 
was  the  time  required  for  equilibrium.  The  hydrogen  was 
purified  by  passing  it  successively  through  alkaline  perman- 
ganate, mercuric  chloride,  alkaline  pyrogallol,  cotton,  and  a 
portion  of  the  same  solution  to  be  measured  placed  in  the 
thermostat. 

The  calculation  of  the  molar  concentration  of  hydrogen 
ion  was  made  by  means  of  the  formula 


DT 

In  this  formula  CH+  is  the  concentration  of  hydrogen  ion, 
E  the  observed  voltage,  T  the  absolute  temperature,  D  a  con- 
stant whose  value  is  .000198,  and  A  a  constant  whose  value 
is  .2342  for  'forty-five  degrees  centigrade. 

Determination  of  the  Percentage  of  Hydration  by  Hydrogen 

Ion  Concentration  Measurements. 

It  is  well  known  that  the  hydration  of  normal  sodium  pyro- 
phosphate  is  represented  by  the  following  equation  : 

Na4P2O7  +  H2O  -+  2Na2HPO4  . 

The  method  used  in  making  the  initial  solutions  for  the  hydra- 
tions  studied  was  to  make  up  a  solution  of  normal  sodium 
pyrophosphate  of  a  certain  concentration  containing  hydro- 
chloric acid  of  a  certain  concentration.  It  was  therefore  pos- 
sible to  make  up  solutions  containing  pyrophosphate,  ortho- 
phosphate  and  hydrochloric  acid  identical  in  composition  with 
any  sample  of  the  particular  solution  in  the  process  of  hydra- 
tion, provided  the  specific  gravity  change  during  hydration 
was  within  the  precision  of  experimental  measurements.  It 
has  been  pointed  out  previously  that  the  specific  gravity 
change  was  not  greater  than  one  part  in  a  thousand  which  is 
within  the  required  accuracy.  Therefore,  it  was  possible  to 
make  up  analytical  curves  by  which  the  hydration  could  be 
followed  by  hydrogen  ion  concentration  measurements.  These 
curves  were  made  up  by  preparing  six  solutions  which  corre- 
sponded in  composition  to  the  initial  solution  being  studied 
and  to  each  twenty  per  cent,  hydration,  the  final  solution 

15 


corresponding  to  complete  hydration.  The  molar  hydrogen 
ion  concentration  measured  on  each  of  these  six  solutions  was 
plotted  against. molar  concentration  of  orthophosphate.  This 
gave  a  curve  from  which,  by  knowing  the  concentration  of 
hydrogen  ion  in  any  particular  solution  being  hydrated,  the 
composition  of  that  solution  could  be  determined  from  the 
curve.  The  data  for  these  curves  are  given  in  Tables  3,  4,  5, 
6,  7,  8,  9,  10,  and  11.  The  curves  are  given  in  plates  I,  II, 
and  III. 

Concentration  of  Na4P207  in  Moles  per  Liter.   I  Division -.025  Mole 
J2$  -100  .075  .050  .025  .000 


3* 


\ 


\ 


PLATE  I 

ANALYTICAL  CURVES 
OF  H,  A  AND  I 


ft -.OS  M.  Na4  P2  07  AND  .425  M.  HCI 
A  -  .725"  M.  Ma*  PZ  Oj  AND  .350  M.  HCI 
AND  .500  M.  HCI 


.050  .100  .150  .200 

Concentration  of  Na2  HP04  in  Moles  per  Liter.  I  Div.-.  050  M. 

16 


.250 


Concentration  ofNa'4  PZ  07  in  Moles  per  L iter.    I Div.  = . 035  Mo/e 
.175  .140  JOS  .070  .035  .000 


.000  .070  .    .140  .210  .260  .350 

Concentration  of  /vs2HP04  /n/wo/es  per  Liter.  I  Div.  ^.070  Mole 

The  materials  used  in  preparing  these  solutions  were  the 
same  as  used  in  preparing  the  hydration  solutions  with  the 
addition  of  the  di-sodium  orthophosphate  which  is  described 
under  preparation  of  materials.  The  method  of  preparing 
these  solutions  was  to  make  up  100  c.c.  in  exactly  the  same 
way  as  described  under  preparation  of  solutions.  The  hydro- 
gen ion  concentration  was  measured  immediately  in  the  same 
way  as  described  under  measurement  of  hydrogen  ion  concen- 
tration. •  The  entire  time  from  the  addition  of  the  acid  until 
the  final  hydrogen  ion  concentration  was  mesaured  was  never 
over  thirty  minutes,  which  introduced  very  little  error  into 
these  measurements  due  to  hydration  during  the  time  of  meas- 
uring corroborated  by  actual  work  of  hydration. 

These  analytical  curves  were  plotted  on  a  scale  such  that 
the  concentration  of  orthophosphate  could  be  read  to  two- 

17 


Concentration  of  Na4  P2  07  in  Moles  per  Liter. 

.180  .135  .090 


. 045  Mole 

045  .000 


PL  AT  EM 

ANALYTICAL  CURVES  E,D&B 

E=  .225  M.  Na+  P2  Of  & .500M.HCI 

D  =  .225  M.  Na4  P2  07  &  425M.HCI 

8  f  .225  M.  Na4  P2  07  Qc.350M.HCI 


.000  .090  .180  .270  .360  .450 

Concentration  of  Na2HP04  in  Moles  per  Liter.    I Div.  -  .090  Mole 

tenths  of  one  per  cent.  In  every  analytical  curve  the  slope 
was  steep  enough  over  the  larger  part  that  a  change  of  two- 
tenths  of  a  millivolt  (the  precision  of  potentiometer  readings) 
in  hydrogen  ion  concentration  measurements  gave  an  error  in 
composition  of  less  than  one  per  cent.,  and  at  the  extreme  end 
where  the  slope  became  less  steep  the  error  was  less  than  two 
per  cent.,  so  that  the  composition  could  be  determined  by  hy- 
drogen ion  concentration  measurements  with  an  accuracy  of 
less  than  two  per  cent,  over  the  entire  curve. 

Separation  of  Ortho  and  Pyrophosphate. 

The  values  for  percentages  of  hydration  as  determined  by 
hydrogen  ion  concentration  measurements  were  checked  over 
the  last  fifty  per  cent,  by  gravimetric  separation.  As  pointed 
out  in  the  introduction,  no  satisfactory  gravimetric  separation 
for  ortho  and  pyrophosphate  was  known.  It  was  known14 

18 


however,  that  pyrophosphate  of  magnesium  was  soluble  in 
magnesium  salts.  A  decision  was  therefore  made  to  attempt  a 
separation  by  use  of  magnesium  chloride  and  magnesium  mix- 
ture. A  number  of  qualitative  determinations  were  made  to 
determine  the  amounts  of  magnesium  chloride  and  magnesium 
mixture  necessary  to  keep  certain  amounts  of  pyrophosphate 
in  solution.  Then  determinations  were  made  to  see  if  ortho- 
phosphate  could  be  precipitated  quantitatively  from  the  mag- 
nesium chloride  mixture  solutions  containing  certain  amounts 
of  dissolved  pyrophosphate. 

TABLE    I. 
Separation  of  Orthophosphate  from  Pyrophosphate 


Mgs.  P 

Mgs.  P 

Mgs.P 

Mgs.  P 

Mgs.P 

Mgs.P 

used  in 

found  in 

used  in 

used  in 

found  in 

used  in 

form  of 

form  of 

form  of 

form  of 

form  of 

form  of 

ortho. 

ortho. 

pyro. 

ortho. 

ortho. 

pyro. 

30.60 

30.38 

40. 

45.00 

45.74 

20. 

30.53 

30.38 

40. 

45.00 

45.91 

20. 

30.53 

30.16 

40. 

45.00 

45.55 

30. 

30.53 

30.75 

40. 

45.00 

45.52 

30. 

30.53 

30.58 

30. 

45.00 

45.29 

30. 

30.53 

30.30 

30. 

45.00 

46.13 

30. 

30.53 

30.61 

30. 

45.00 

45.77 

20. 

30.53 

30.53 

20. 

45.00 

45.91 

20. 

30.53 

30.38 

20. 

45.00 

44.83 

none 

45.00 

45.20 

30. 

45.00 

44.74 

none 

45.00 

44.83 

none 

45.00 

46.41 

30. 

45.00 

44.52 

none 

45.00 

45.88 

30. 

44.90 

45.69 

30. 

21.60 

21.74 

30. 

45.00 

46.41 

30 

21.60 

21.49 

30. 

45.00 

45.88 

30. 

In  Table  1  it  is  shown  that  from  30  to  45  milligrams  of  phos- 
phorus as  orthophosphate  can  be  determined  within  two  per 
cent,  in  the  presence  of  40  milligrams  or  less  of  phosphorus  as 
pyrophosphate.  Attempts  to  determine  orthophosphate  in 
greater  concentrations  of  pyrophosphate  were  not  successful 
because  of  the  large  amounts  of  the  magnesium  chloride  mix- 
ture necessary  to  keep  the  pyrophosphate  in  solution  which 
made  the  method  cumbersome  and  inaccurate. 

19 


The  following  method  for  separation  was  developed:  170 
c.c.  of  magnesium  mixture  and  85  c.c.  of  magnesium  chloride 
solution  (described  under  preparation  of  materials)  were 
mixed  just  before  using.  This  mixture  of  the  two  solutions 
has  been  called  throughout  this  article  "the  magnesium  chlor- 
ide mixture."  The  pyrophosphate  was  dissolved  in  a  few  c.c. 
of  water  and  added  slowly  with  continuous  stirring  to  the 
magnesium  chloride  mixture  and  stirred  until  any  precipitate 
which  formed  was  re-dissolved.  The  orthophosphate  solution 
was  added  slowly  with  continuous  stirring  from  a  burette. 
The  solution  was  then  stirred  until  the  precipitate  became 
crystalline.  It  was  then  allowed  to  stand  from  twelve  to  four- 
teen hours,  then  filtered  and  washed  with  an  ammonium  ni- 
trate and  ammonium  hydroxide  solution.  This  precipitate 
was  then  dissolved  in  cold  six  molar  hydrochloric  acid  and  re- 
precipitated  by  adding  twenty  c.c.  of  15  M.  ammonium  hy- 
droxide and  a  few  c.c.  of  magnesium  mixture,  stirring  well 
during  precipitation.  It  was  allowed  to  stand  from  six  to 
twelve  hours,  then  filtered  into  a  Gooch  crucible  and  ignited 
and  weighed  as  magnesium  pyrophosphate. 

By  this  method  it  was  possible  to  precipitate  the  ortho- 
phosphate  in  a  crystalline  form.  In  most  cases  however,  the 
first  precipitate  showed  traces  of  pyrophosphate  which  forms 
a  gelatinous  precipitate  with  magnesium  mixture.  To  mini- 
mize as  much  as  possible  hydrating  this  pyrophsophate  to  the 
orthophosphate  during  the  dissolving  of  the  precipitate  with 
acid,  cold  acid  was  used  and  the  solution  run  directly  into  the 
ammonium  hydroxide  used  for  re-precipitation.  In  spite  of 
these  precautions  a  small  amount  of  pyrophosphate  was  hy- 
drated  during  the  operation  as  may  be  seen  in  Table  1,  where 
a  majority  of  the  values  show  a  slight  increase  in  orthophos- 
phate over  that  taken  in  the  sample. 

This  method  of  separation  can  be  used  where  the  concen- 
tration of  phosphorus  as  pyrophsophate  does  not  exceed  about 
45  milligrams  and  the  concentration  of  phosphorus  as  ortho- 
phosphate  is  about  30  to  45  milligrams  in  the  total  volume  of 
160  c.c.  used.  The  limits  of  this  method  allow  its  use  then 
only  after  the  pyrophosphate  solutions  are  over  fifty  per  cent, 
hydrated  and  it  was  therefore  used  to  check  the  values  ob- 

20 


tained  b'y  hydrogen  ion  measurements  over  the  last  fifty  per 
cent. 

The  method  of  sampling  and  analyzing  the  solutions  being 
rn-drated  was  as  follows : 

The  concentration  of  the  hydrogen  ion  was  measured  as  de- 
scribed under  measurement  of  hydrogen  ion  concentration  at 
intervals  of  about  every  eight  to  ten  per  cent  hydration. 
After  the  solutions  were  over  fifty  per  cent  hydrated  gravi- 
metric samples  were  taken  at  the  same  time  as  the  hydrogen 
iov>  concentration  samples.  These  samples  were  taken  by 
means  of  a  Bailey  weighing  burette.  An  effort  was  made  to 
get  samples  in  which  the  phosphorus  as  orthophosphate  was 
within  30  to  45  milligrams.  The  sample  was  added  drop  by 
drop  with  constant  stirring  to  the  magnesium  chloride  mix- 
ture. When  these  samples  containing  both  ortho  and  pyro- 
phosphate were  added  a  curdy  precipitate  of  ortho  with  some 
pyrophosphate  was  formed.  In  order  to  re-dissolve  the  pyro- 
phosphate  it  was  necessary  to  stir  for  some  time  until  the  pre- 
cipitate became  distinctly  crystalline  and  no  curdy  precipitate 
could  be  observed.  The  lengths  of  time  to  accomplish  this 
varied,  but  thirty  minutes  was  usually  sufficient. 

In  this  way  two  values  were  obtained  for  the  percentage  of 
hydration  over  the  last  fifty  per  cent.  By  referring  to  the 
tables  under  experimental  data  it  may  be  seen  that  the  first 
gravimetric  samples  gave  values  which  were  usually  three  to 
five  per  cent,  higher  than  those  obtained  by  hydrogen  ion  con- 
centration measurements,  and  as  the  hydration  neared  com- 
pletion and  the  concentration  of  pyrophosphate  became  less 
the  agreement  between  the  two  values  became  better  and  near 
completion  checked  within  the  experimental  limits.  The  rea- 
son for  the  greater  deviation  at  first  is  due  to  the  pyrophos- 
phate carried  down  in  the  first  precipitation  which  was  partly 
hydrated  on  dissolving  in  acid  for  the  second  precipitation. 
It  was  found  more  difficult  to  re-dissolve  the  pyrophosphate 
in  these  samples  than  it  was  when  it  was  added  alone  as  was 
done  in  the  development  of  the  separation,  and  with  the 
utmost  precaution  the  first  precipitates  when  filtered  always 
showed  the  presence  of  a  little  pyrophosphate.  Then  as  the 
pyrophosphate  concentration  in  the  samples  decreased  the 

21 


amount  carried  down  was  much  less  and  agreement  'was  ob- 
tained in  the  values  by  both  methods.  So  by  use  of  this  gravi- 
metric method  it  was  possible  to  have  a  check  over 'the  last 
fifty  per  cent,  on  the  values  obtained  by  the  hydrogen  ion 
concentration  measurements. 

It  can  be  seen  by  a  comparison  of  the  tables  that  the  hy- 
drogen ion  concentration  in  each  solution  approached  a  final 
value  very  nearly  the  same  as  the  value  obtained  for  the 
analytical  curves  where  the  final  solution  was  made  up  of  di- 
sodium,  orthophosphate  and  hydrochloric  acid.  Every  solu- 
tion was  left  in  the  thermostat  from  two  weeks  to  a  month 
and  the  hydrogen  ion  concentration  measured  two  or  three 
times  after  the  final  value  which  is  given  in  the  tables  was 
obtained,  and  in  every  case  the  hydrogen  ion  concentration 
remained  constant  which  shows  that  equilibrium  had  been 
reached. 

In  determining  orthophosphate  by  magnesium  mixture  it 
is  usually  difficult  to  get  perfectly  white  ignited  precipitates. 
Nearly  all  show  black  spots  after  they  have  been  ignited  to 
the  magnesium  pyrophosphate.  It  was  thought  this  might  be 
due  partly  to  suspended  organic  matter  in  the  reagents  or 
from  such  material  in  the  air  getting  into  the  precipitate  be- 
fore it  was  ignited.  To  see  if  extra  precautions  to  avoid  con- 
tamination of  the  precipitates  in  this  way  would  decrease  the 
black  spots  after  ignition,  all  reagents  used  in  .the  final  pre- 
cipitation and  washing  were  filtered  and  the  precipitate  pro- 
tected from  dust  and  dirt  from  the  air  as  much  as  possible. 
These  precautions  were  taken  throughout  this  work  and  the 
majority  of  the  precipitates  were  white,  showing  no  black 
spots. 

EXPERIMENTAL  DATA 

In  the  following  table  are  outlined  the  solutions  of  normal 
sodium  pyrophosphate  and  hydrochloric  acid  studied  in  se- 
curing the  data  for  the  hydration  and  for  the  effect  of  hydro- 
gen ion  concentration  upon  the  rate  of  the  hydration. 

22 


Solution 


TABLE    2. 
Solutions  Studied 

Concentration  of  Concentration  of 

Na4P9O7  in  moles  HC1  in  moles 

per  Liter  at  20°  C.       per  Liter  at  20°  C. 


.125 
.125 
.125 
.125 
.125 
.125 
.175 
.175 
.175 
.175 
.175 
.175 
.225 
.225 
.225 
.225 
.225 
.225 


.350 
.350 
.425 
.425 
.500 
.500 
.350 
.350 
.425 
.425 
.500 
.500 
.350 
.350 
.425 
.425 
.500 
.500 


Specific 
Gravity 
at  20°  C. 
1.029 
1.029 
1.030 
1.030 
1.031 
1.031 
1.041 
1.040 
1.041 
1.041 
1.043 
1.043 
1.052 
1.052 
1.054 
1.054 
1.056 
1.056 


It  may  be  observed  in  the  above  outline  that  all  hydra- 
tions  were  run  in  duplicate.  In  every  case  the  two  checked 
within  experimental  error  and  therefore  the  data  for  only  one 
is  given. 

All  synthetic  solutions  for  analytical  curves  are  lettered 
the  same  as  the  respective  solutions  to  be  hydrated. 

TABLE    3. 

Data  for  Analytical  Curve  I  in  Plate  I. 
Concentration  of  HC1  =  .500  M.  at  20°  C. 

Temperature  =  45°  C. 
Barometric  Pressure  =  766.0  mm.  at  19°  C. 

Molar 
Concentration 


Solution 
1 
2 
3 
4 
5 
6 


of  Na4P2O_ 
at20°C. 
.125 
.100 
.075 
.050 
.025 
.000 


Molar 

Molar 

Concentration 

Concentration 

of  Na2HPO4 

Voltage 

of  Hydrogen 

at  20°  C. 

E 

Ion  X  102 

.000 

.2892 

13.39 

.050 

.2919 

12.14 

.100 

.2958 

10.52 

.150 

.2999 

9.06 

.200 

.3056 

7.36 

.250 

.3112 

5.99 

23 


Solution 
1 
2 
3 
4 
5 
6 


Solution 
1 
2 
3 
4 
5 
6 


Solution 
1 
2 
3 
4 
5 
6 


TABLE   4. 

Data  for  Analytical  Curve  H  in  Plate  I. 
Concentration  of  HC1  =  .425  M.  at  20°  C. 

Temperature  =  45°  C. 
Barometric  Pressure  =  758.0  mm.  at  21.5°  C. 


Molar 

Molar 

Molar 

oncentration 

Concentration 

Concentration 

of  Na4P2O7 

at20°C.  ' 

of  Na2HPO4 
at20°'C. 

Voltage 
E 

of  Hydrogen 
Ion  X  103 

.125 

.000 

.3080 

67.4 

.100 

.050 

.3137 

54.7 

.075 

.100 

.3211 

41.8 

.050 

.150 

.3278 

32.6 

.025 

.200 

.3322 

27.7 

.000 

.250 

.3379 

22.6 

TABLE   5. 

Data  for  Analytical  Curve  A  in  Plate  I. 
Concentration  of  HC1  =  .350  M.  at  20°  C. 

Temperature  =  45°  C. 
Barometric  Pressure  —  744.0  mm.  at  21°  C. 


Molar 

Molar 

Molar 

oncentration 

Concentration 

Concentration 

of  Na4P2O7 

at20°C. 

of  Na2HPO4 
at  20°  C. 

Voltage 
E 

of  Hydrogen 
Ion  X  103 

.125 

.000 

.3313 

28.7 

.100 

.050 

.3392 

21.6 

.075 

.100 

.3470 

16.4 

.050 

.150 

.3535 

12.8 

.025 

.200 

.3597 

10.0 

.000 

.250 

.3646 

8.5 

TABLE   6. 

Data  for  Analytical  Curve  G  in  Plate  II. 
Concentration  of  HC1  =  .500  M.  at  20°  C. 

Temperature  =  45°  C. 
Barometric  Pressure  =  764.0.  mm.  at  20.5 

Molar  Molar 

Concentration     Concentration 
of  Na2HPO 
at  20°  C. 


of  Na4P207 
at20°C. 


.175 
.140 
.105 
.070 
.035 
.000 


.000 
.070 
.140 
.210 
.280 
.350 


C. 

Molar 

Concentration 
Voltage*    of  Hydrogen 
Ion  X  103 
43.3 
31.8 
23.6 
17.7 


E 

.3201 
.3285 
.3367 
.3445 
.3509 
.3565 


14.0 
11.4 


24 


Solution 
1 
2 
3 
4 
5 
6 


Solution 
1 
2 
3 
4 
5 
6 


TABLE   7. 

Data  for  Analytical  Curve  F  in  Plate  II. 
Concentration  of  HC1  =  .425  M.  at  20°  C. 

Temperature  =  45°  C. 
Barometric  Pressure  =  766.0  mm.  at  19.5°  C. 


Molar 

Molar 

Molar 

Concentration 

Concentration 

Concentration 

of  Na4P007 
at20°C. 

of  Na2HP04 
at  20°  C. 

Voltage 
E 

of  Hydrogen 
Ion  X  103 

.175 

.000 

.3557 

11.80 

.140 

.070 

.3661 

8.06 

.105 

.140 

.3738 

6.08 

.070 

.210 

.3809 

4.58 

.035 

.280 

.3865 

3.82 

.000 

.350 

.3910 

3.24 

TABLE    8. 

Data  for  Analytical  Curve  C  in  Plate  II. 
Concentration  of  HC1  =  .350  M.  at  20°  C. 

Temperature  =  45°  C. 
Barometric  Pressure  =  759.0  mm.  at  19.5°  C. 


Molar 

Molar 

Molar 

Concentration 

Concentration 

Concentration 

of  Na4P207 

of  Na2HPO4 

Voltage 

of  Hydrogen 

Solution 

at20°C. 

at20°C. 

E 

Ion  X  106 

1 

.175 

.000 

.4961 

69.6 

2 

.140 

.070 

.4966 

61.3 

3 

.105 

.140 

.5038 

52.5 

4 

.070 

.210 

.5086 

44.1 

5 

.035 

.280 

.5149 

35.0 

6 

.000 

.350 

.5235 

25.5 

TABLE  9. 

Data  for  Analytical  Curve  E  in  Plate  III. 
Concentration  of  HC1  =  .500  M.  at  20°  C. 

Temperature  =  45°  C. 
Barometric  Pressure  =  770.0  mm.  at  18°  C. 


Molar 
Concentration 


Molar 
Concentration 


ofNa.P  O         ofNaHPO, 


at20°C. 
.225 
.180 
.135 
.090 
.045 
.000 


at20°C 
.000 
.090 
.180 
.270 
.360 
.450 


Voltage 

E 

.3767 
.3883 
.3970 
.4036 
.4101 
.4138 


Molar 

Concentration 

of  Hydrogen 

Ion  X  103 

5.45 

3.58 

2.61 

2.05 

1.61 

1.41 


25 


Solution 
1 
2 
3 
4 
5 
6 


TABLE    10. 

Data  for  Analytical  Curve  D  in  Plate  III. 
Concentration  of  HC1  =  .425  M.  at  20°  C. 

Temperature^  45°  C. 
Barometric  Pressure  =  752.0  mm.  at  19°  C. 


Molar 

Molar 

Molar 

Concentration 

Concentration 

Concentration 

of  Na4P0O. 

of  Na9HPO4 

Voltage 

of  Hydrogen 

Solution 

at20°C.  ' 

at  20°  C. 

E 

Ion  X  106 

1 

.225 

.000 

.5273 

22.2 

2 

.180 

.090 

.5315 

19.1 

3 

.135 

.180 

.5354 

16.5 

4 

.090 

.270 

.5402 

13.9 

5 

.045 

.360 

.5468 

10.9 

6 

.000 

.450 

.5522 

9.0 

TABLE  11. 

Data  for  Analytical  Curve  B  in  Plate  III. 

Concentration  of  HC1  =  .350  M.  at  20°  C. 

Temperature  =  45°  C. 


rometric  Pressure  =  762.0  mm 

.  at  19°  C. 

Molar 

Molar 

Molar 

Concentration 

Concentration 

Concentration 

of  Na4P90_ 

of  Na2HPO4 

Voltage 

of  Hydrogen 

at20°C. 

at20°C. 

E 

Ion  X  106 

.225 

.000 

.5742 

4.10 

.180 

.090 

.5775 

3.55 

.135 

.180 

.5818 

3.04 

.090 

.270 

.5857 

2.63 

.045 

.360 

.5887 

2.36 

.000 

.450 

.5903 

2.22 

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Concentration  in  Moles  per  Liter.  IDiv.~.05Mole.  Na2HP04&  Hydrogen  Ion 
.00  -  .05  .10 


.15 


.20 


36 


DISCUSSION 
Change  of  Hydrogen  Ion  Concentration  During  Hydration. 

By  adding  acid  directly  to  the  normal  sodium  pyrophos- 
phate  solutions  it  was  possible  to  obtain  any  desired  concen- 
tration of  hydrogen  ion  and  determine  its  influence.  In  order 
to  show  this  influence  the  hydration  curves  of  one  concentra- 
tion of  normal  sodium  pyrophosphate  in  the  three  different 
acid  concentrations  used  have  been  plotted  on  one  plate.  All 
hydration  curves  are  plotted  from  the  results  obtained  by 

Concentration  in  Moles  per  Liter.  IDiv.=.07Mole.  NazHP04  &  Hydrogen  Ion 

.00  .07  .14  '.21  .28  35 


hydrogen  ion  concentration  measurements  except  the  last  two 
points  on  curve  D  in  which  the  hydrogen  ion  concentration 
measurements  did  not  agree  with  the  gravimetric  determina- 
tions used. 

On  plate  IV  are  plotted  the  hydration  curves  of  .125  M. 
normal  sodium  pyrophosphate  in  .350  M.,  .425  M.,  and  .500  M. 
hydrochloric  acid,  and  on  plates  V  and  VI  are  plotted  the 
hydration  curves  of  .175  M.  and  .225  M.  normal  sodium  pyro- 
phosphate respectively  in  each  of  the  three  concentrations  of 
acid.  On  the  same  plates  are  plotted  the  hydrogen  ion  con- 
centration curves  for  each  of  the  solutions.  The  hydrogen 
ion  concentrations  have  been  multiplied  by  values  such  that 
they  could  be  plotted  on  the  same  concentration  scale  as  the 
hydration  curves,  thus  showing  the  relative  decrease  in  hy- 
drogen ion  concentration  as  the  hydration  proceeded.  From 
these  hydrogen  ion  concentration  curves  in  the  three  plates  it 
is  seen  that  in  every  solution  there  was  a  gradual  decrease  in 
hydrogen  ion  concentration  as  the  hydration  proceeded, — 


30  60 

Time  in  Days 


90  120 

/Division  -30  Days 


38 


finally  reaching  a  constant  value  at  completion.  The  gradual 
decrease  of  hydrogen  ion  concentration  as  the  concentration 
of  orthophosphate  gradually  increased  is  accounted  for  by  the 
less  dissociated  orthophosphoric  acid. 

By  referring  to  the  tables  of  data  for  the  analytical  curves 
it  is  seen  that  in  the  same  hydrochloric  acid  concentration  an 
increase  both  of  pyrophosphate  and  of  orthophosphate  causes 
a  decrease  in  hydrogen  ion  concentration.  So  it  was  possible 
by  the  use  of  three  concentrations  of  pyrophosphate  and  three 
concentrations  of  acid  to  have  nine  solutions  of  different  hy- 
drogen ion  concentration  and  in  that  way  to  study  the  effect 
of  the  hydrogen  ion  concentration  on  the  rate  of  hydration. 

By  a  comparison  of  the  hydration  curves  in  the  three 
plates,  and  of  the  data  for  these  curves  given  in  the  tables  for 
the  different  solutions  it  may  be  seen  that  the  times  required 
for  equilibrium  within  experimental  error  for  .125  M.  Na4P2O7 
solution  with  .500  M.,  .425  M.,  and  .350  M.  HC1  were  respec- 
tively 250  hours,  702  hours,  and  1,302  hours;  for  a  .175  M. 
Na4P,O7  solution  with  .500  M.,  .425  M.,  and  .350  M.  HC1  the 
times  for  equilibrium  were  1,160  hours,  1,493  hours  and  2,386 
hours  respectively ;  and  for  a  .225  M.  Na4P2O7  solution  with 
.500  M.  and  .425  M.  HC1  the  times  for  equilibrium  were  1,688 
hours  and  2,719  hours  respectively ;  and  for  .225  M.  Na4P2O7 
solution  with  .350  M.  HC1,  2,766  hours  were  required  for 
81%  hydration.  If  it  continued  at  the  rate  at  which  it  was 
going  over  the  last  20  per  cent.,  it  would  require  at  a  mini- 
mum three  months  longer  for  completion. 

From  a  comparison  of  the  hydrogen  ion  concentrations 
in  these  solutions  it  is  observed  that  the  solutions  of  highest 
initial  hydrogen  ion  concentration  required  the  least  time 
for  equilibrium,  the  time  increasing  as  the  initial  hydrogen 
ion  concentration  decreased.  This  was  also  shown  in  the 
hydration  of  sodium  monometaphosphate8.  These  times 
show  the  great  influence  that  hydrogen  ion  has  upon  this 
hydration. 

Effect  of  Concentration  of  Pyrophosphate  on  the  Rate  of 
Hydration. 

Abbott9  from  his  investigation  of  the  hydration  of  pyro- 
phosphoric  acid  calculated  the  rate  of  hydration  (1)  "on  the 

39 


assumption  that  the  rate  of  hydration  is  proportional  both 
to  the  hydrogen  ion  concentration  and  to  that  of  the  pyro- 
phosphoric  acid  undergoing  hydration,"  and  (2)  "on  the 
assumption  that  the  rate  is  independent  of  the  hydrogen  ion 
concentration  and  is  determined  only  by  the  concentration  of 
the  pyrophosphoric  acid."  The  constants  calculated  on  the 
second  assumption  were  more  nearly  constant  and  he  con- 
cludes from  that,  that  the  rate  of  hydration  is  approximately 
proportional  to  the!  concentration  of  pyrophosphoric  acid 
present  and  that  it  increases  with  the  concentration  of 
hydrogen  ion. 

To  see  if  the  reaction  studied  in  this  investigation  was  of 
the  first  order  and  if  constants  calculated  for  a  first  order 
reaction  would  be  of  value  in  studying  it,  they  have  been 
calculated  from  the  first  determination  for  each  solution 

1          C— xt 

hydrated  according  to  the  formula  K= log where 

tx-tl        C-x 

C  is  the  original  concentration  of  pyrophosphate  and  x  the 
amount  changed  to  orthophosphate  in  time  t.  This  assumes 
then  that  the  rate  of  hydration  is  a  direct  function  of  the 
concentration  of  pyrophosphate.  These  constants  are  given 
in  the  tables  of  data  for  each  solution ;  they  show  a  pro- 
gressive decrease  as  the  hydrogen  ion  concentration  shows 
a  progressive  decrease  from  the  solutions  which  have  the  low- 
est concentration  of  pyrophosphate  and  highest  concentra- 
tion of  hydrogen  ion  down  to  the  solutions  having  the  high- 
est concentration  of  pyrophosphate  and  lowest  concentration 
of  hydrogen  ion,  both  in  the  individual  solutions  and  among 
the  solutions  except  in  solutions  C  and  D  where  they  ap- 
proach more  nearly  a  constant  value. 

From  this  decrease  in  the  constants  it  is  evident  that  the 
rate  of  hydration  of  normal  sodium  pyrophosphate  in  the 
presence  of  hydrogen  ion  is  not  a  direct  function  of  the  pyro- 
phosphate concentration  alone.  It  is  increased  by  the  hy- 
drogen ion  present  and  as  the  hydrogen  ion  concentration 
decreases  the  rate  decreases. 

In  Table  23  for  solution  C2  in  which  the  ratio  of  pyro- 
phosphate to  hydrochloric  acid  is  1  mole  to  2  moles,  the  con- 

40 


stants  do  not  decrease  regularly  but  tend  to  approach  a  con- 
stant. The  mean  value  of  these  constants  has  been  calcu- 
lated and  is  given  in  the  table.  This  mean  neglects  point 
four  which  is  probably  in  error  as  shown  by  the  hydration 
curve,  and  also  the  first  and  last  values  which  are  less  ac- 
curate in  most  of  the  tables.  In  the  last  column  of  that  table 
are  the  percentages  of  deviation  of  each  of  the  constants 
from  the  mean.  In  this  column  it  is  shown  that  eight  and 
four-tenths  per  cent,  is  the  greatest  deviation  from  the  mean 
while  most  of.  the  values  are  within  four  to  five  per  cent. 
Constants  were  calculated  for  some  of  the  value  by  using  a 
value  for  the  percentage  hydrated  at  time  t  two  per  cent, 
greater  than  that  determined  and  given  in  the  table.  It  was 
found  that  this  change  of  two  per  cent,  caused  an  increase 
in  the  value  of  the  constant  from  five  to  ten  per  cent.,  de- 
pending on  what  part  of  the  curve  the  value  was  selected. 

While  it  may  seem  that  values  for  the  constants  in  solu- 
tion C2  are  tending  to  approach  a  constant  within  experi- 
mental error,  they  are,  however,  still  tending  to  show  a  very 
small  decrease.  It  does  not  seem  then  that  the  rate  of  hydra- 
tion in  this  solution  can  be  said  to  be  directly  proportional 
to  the  pyrophosphate  concentration  but  to  approach  it  very 
closely. 

In  Table  26  for  solution  D  where  the  ratio  of  pyrophos- 
phate to  acid  is  1  mole  to  1.888  moles,  the  constants  are  also 
quite  constant.  The  mean  value  and  percentage  deviations 
from  it  have  been  calculated  and  are  given  in  the  table  as 
described  above  for  solution  C.  The  error  caused  by  two 
per  cent,  change  in  percentages  hydrated  is  from  five  to 
ten  per  cent,  in  this  solution  as  in  solution  C.  It  is  seen  that 
in  this  solution  the  constants  are  also  tending  to  approach  a 
constant  value  within  experimental  error  but  as  in  solution 
C  the  constants  are  tending  to  show  a  small  decrease  so  that 
the  rate  of  hydration  in  this  solution  also  is  not  quite  a  di- 
rect function  of  the  pyrophosphate  concentration  alone  but 
is  approaching  it. 

Since  the  constants  for  solutions  C  and  D  where  the  ratio 
of  pyrophosphate  to  acid  is  about  1  mole  to  2  moles  are  very 
nearly  constant1  and  in  all  other  solutions  the  constants  show 

41 


a  gradual  decrease,  it  seems  that  two  influences  must  be 
active  in  this  hydration.  Any  discussion  of  the  mechanism 
of  the  reaction  is  necessarily  limited  by  the  lack  of  the  ioni- 
zation  constants  of  pyrophosphoric  and  orthophosphoric 
acids  at  this  temperature  and  by  the  lack  of  a  method  for 
determining  the  concentration  of  any  of  the  respective  pyro 
and  orthophosphate  ions.  The  results  show  that  hydrogen 
ion  has  a  marked  influence  on  the  rate  of  hydration  and  as 
the  concentration  of  hydrogen  ion  decreases  the  rate  also  de- 
creases. Therefore  if  the  hydrogen  ion  was  the  only  factor 
in  this  hydration,  the  constants  as  calculated  should  show  a 
progressive  decrease  as  the  hydrogen  ion  concentration 
shows  a  progressive  decrease.  Since  the  constants  do  not 
show  this  decrease  in  solutions  C  and  D,  some  influence  must 
be  at  work  in  the  reaction  to  balance  the  decreasing  influence 
of  the  hydrogen  ion. 

In  this  investigation  where  the  concentration  of  hydro- 
gen ion  was  not  sufficient  in  most  of  the  solutions  to  form 
very  much  pyrophosphoric  acid  it  seems  that  the  active  com- 
ponent undergoing  hydration  must  be  one  of  the  ionic  prod- 
ucts of  pyrophosphoric  acid,  as  the  pyrophosphoric  acid» 
would  decrease  as  the  hydrogen  ion  concentration  decreased. 
If,  then,  the  active  component  undergoing  hydration  is  one 
of  the  ions,  the  rate  of  hydration  would  therefore  depend 
in  part  on  the  concentration  of  that  ion.  It  then  follows  that 
hydrogen  ion  should  show  a  slight  negative  influence  on  this 
hydration  due  to  repression  of  the  active  ion.  The  negative 
influence  of  hydrogen  ion  must  be  very  slight  compared  to 
the  positive  influence  because  the  results  show  the  higher  the 
concentration  of  hydrogen  ion  the  greater  is  the  rate  of  hy- 
dration. It  seems  not  impossible,  however,  that  an  initial 
concentration  of  hydrogen  ion  and  of  pyrophosphate  might 
be  obtained  in  which  the  removal  of  a  very  small  amount  of 
hydrogen  ion  would  result  in  the*  formation  of  a  much  larger 
corcentration  of  this  active  ion  undergoing  the  hydration  and 
therefore  as  the  influence  of  the  hydrogen  ion  on  the  hydra- 
tion decreased  the  effect  of  the  active  ion  would  increase  and 
the  two  balance  each  other.  This  seems  to  be  the  case  in  solu- 

42 


tions  D  and  C  where  the  constants  obtained  for  a  firaj^prder 
reaction  show  a  very  slight  decrease  in  their  values. 

The  curves  obtained  by  plotting  molar  concentration  of 
pyrophosphate  against  molar  concentration  of  hydrogen  ion 
are  straight  lines  or  very  nearly  so  for  solutions  C,  D,  and  I. 
Therefore  the  hydrogen  ion  concentration  in  these  solutions 
is  apparently  directly  proportional  to  the  pyrophosphate  con- 
centration as  the  hydration  proceeds.  Similar  curves  for  the 
other  solutions  are  not  straight  lines  but  show  decreasing 
slopes  as  the  pyrophosphate  concentration  decreases.  Since 
the  orthophosphoric  acid  ions  H2PO4~  and  HPO4~  are  much 
less  dissociated  than  the  respective  pyrophosphoric  acid  ions 
H2P2O7~  and  HP2O7~,  it  follows  that  in  order  for  the  pyro- 
phosphate concentration  to  show  a  constant  ratio  to  the  hy- 
drogen ion  concentration  that  the  pyro  phosphoric  acid  ions 
must  maintain  a  sufficient  concentration  of  hydrogen  ion 
through  dissociation  to  keep  the  ratio  constant,  as  the  hydro- 
gen ion  concentration  is  being  decreased  in  forming  the  less 
dissociated  orthophosphoric  acid  ions.  Therefore  the  rate  of 
dissociation  of  the  pyrophosphoric  acid  ions  must  continu- 
ally increase  as  the  orthophosphate  is  formed. 

If  as  postulated  the  active  principle  undergoing  hydration 
is  one  of  the  ions  of  pyrophosphoric  acid  it  is  evident  then 
that  its^  positive  influence  would  increase  as  the  hydration 
proceeded  and  this  influence  might  approach  a  value  sufficient 
to  counterbalance  the  decreasing  influence  of  hydrogen  ion 
upon  the  hydration  and  therefore  give  a  constant  value  for  the 
constants  as  calculated  for  a  first  order  reaction.  From  the 
greater  influence  which  hydrogen  ion  has  upon  the  reaction, 
its  decrease  could  only  be  counterbalanced  by  the  positive 
influence  of  pyrophosphate  concentrations  in  solutions  in 
which  the  initial  hydrogen  ion  concentration  was  relatively 
small  as  in  solution  D  where  it  was  22.1  X  10"6  moles  per  liter 
and  in  solution  C  where  it  was  69.4  X  1O6  moles  per  liter. 
Whereas  in  solution  I  where  the  initial  hydrogen  ion  concen- 
tration was  13.4  X  10-2  moles  per  liter  and  the  ratio  of  acid 
was  four  moles  to  one  mole  of  pyrophosphate,  the  curve  is  a 
straight  line  but  the  the  constants  show  a  progressive  de- 
crease. This  seems  to  point  to  the  conclusion  that  one  of  the 

43 


lower  acid  ions  of  pyrophosphoric  acid  or  the  pyrophosphate 
ion  is  the  active  component  undergoing  hydration  and  that 
the  influence  of  its  concentration  is  very  small  compared  to 
the  influence  of  hydrogen  ion.  It  appears,  therefore,  that  in 
the  higher  concentrations  of  hydrogen  ion  the  formation  of 
the  active  ion  undergoing  hydration  is  not  sufficient  to  coun- 
terbalance the  decreasing  influence  of  the  hydrogen  ion  con- 
centration and  accordingly  the  constants  calculated  show  a 
progressive  decrease. 

In  solution  B,  however,  the  ratio  of  acid  to  pyrophosphate 
was  1.555  moles  to  1  mole  and  the  initial  hydrogen  ion  con- 
centration was  4.1  X  10~8  moles  per  liter.  So  the  influence  of 
the  hydrogen  ion  upon  the  repression  of  the  active  ion  is  less 
at  the  start  than  in  solutions  C  and  D.  Therefore  as  the  hy- 
drogen ion  concentration  decreases  and  its  influence  decreases 
it  ib  not  balanced  by  the  formation  of  an  appreciably  greater 
concentration  of  the  active  ion.  Accordingly  in  this  solution 
the  constants  show  a  progressive  decrease. 

In  the  foregoing  discussion  of  the  hydration  in  solutions 
C,  D,  and  I,  it  was  pointed  out  that  the  concentration  of  hy- 
drogen ion  was  directly  proportional  to  the  pyrophosphate 
concentration.  Therefore  it.  is  possible  to  express  the  con- 
centration of  hydrogen  ion  in  terms  of  pyrophosphate  concen- 
tration. By  doing  this  and  by  assuming  that  the  rate  of 
hydration  is  a  direct  function  of  both  the  pyrophosphate  con- 
centration and  the  hydrogen  ion  concentration  it  is  possible 
to  formulate  an  expression  which  would  give  the  influence  of 
the  changing  hydrogen  ion  concentration  at  any  instant  in  the 
hydration. 

With  this  assumption  the  following  development  is  made : 

dx 

—  =  K1(c-x)CH. 
dt 

c  =  molar  concentration  of  pyrophosphate. 
x  =  amount  of  pyrophosphate  changed  in  any  time  t. 
CH+=a(c— x)+K2 

a  =  the  slope  of  the  line. 

K2  =  hydrogen  ion  concentration  at  complete  hydration. 
This  equation  represents  the  concentration  of  hy- 
drogen ion  at  any  time  t. 

44 


.-.--=K1(c-x)(a(c-x)+K2) 

The  integration  of  the  above  expression  between  the  limits 
tx  and  tx  gives  the  following  formula : 

1  (K4-X)(c-Xl) 

K,  = log 

(ti-OK,  (c-xXK.-XJ 

K—  
4  ~ 

a 

Using  this  formula  constants  have  been  calculated  for 
solutions  Ij,  C2,  and  Dx.  They  are  given  in  the  last  column 
of  Tables  12,  23,  and  26  respectively. 

In  Solution  I  the  concentration  of  pyrophosphate  was 
.125  M.  and  the  concentration  of  hydrochloric  acid  was  .500 
M.  The  change  of  hydrogen  ion  concentration  was  from 
13.35  X  10-2  to  6.10  X  10-2  moles  per  liter.  The  constants  cal- 
culated by  this  formula  show  a  slight  tendency  to  decrease  as 
they  do  when  calculated  on  the  assumption  that  the  rate  of 
hydration  is  directly  proportional  to  the  pyrophosphate  con- 
centration alone. 

In  solution  C2  the  constants  show  a  progressive  increase. 
In  this  solution  the  concentration  of  pyrophosphate  was  .175 
M.  and  the  hydrochloric  acid  was  .350  M.  The  change  of 
hydrogen  ion  concentration  was  from  69.4  XlO~6  to  27.3  X  10~6 
moles  per  liter. 

In  solution  Dx  the  constants  decrease  to  a  minimum  and 
then  increase  to  their  former  values.  In  this  solution  the  con- 
centration of  pyrophosphate  was  .225  M.  and  the  concentra- 
tion of  hydrochloric  acid  was  .425  M.  The  change  of  hydro- 
gen ion  concentration  was  from  22.3  X  10-°  to  10.0  X  1Q-6 
moles  per  liter. 

In  solution  Ix  the  concentration  of  pyrophosphate  was  low 
and  the  hydrogen  ion  concentration  was  high.  In  solution 
D!  the  pyrophosphate  concentration  was  high  and  the  hydro- 
gen ion  concentration  was  low.  In  solution  C2  the  pyrophos- 
phate concentration  was  between  that  of  solutions  I2  and  Dlf 
and  the  hydrogen  ion  concentration  was  a  little  greater  than 
that  of  D!.  The  constants  for  solution  I  by  both  formulas 

45 


show  about  the  same  decrease.  In  solutions  C2  and  Da  by  the 
first  formula  the  constants  approach  quite  closely  a  constant 
value.  By  the  second  formula  in  solution  C2  they  show  a  pro- 
gressive increase.  In  solution  Dl  they  pass  through  a 
minimum. 

From  this  study  then  the  results  seem  to  point  to  the  con- 
clusion that  one  of  the  ionic  products  of  pyrophosphoric  acid, 
possibly  the  pyrophosphate  ion,  is  the  active  component  un- 
dergoing hydration  and  that  hydrogen  ion  shows  a  slight 
negative  influence  due  to  the  repression  of  this  active  compo- 
nent but  this  negative  influence  is  only  very  slight  compared 
to  the  positive  influence  shown  by  the  hydrogen  ion.  There- 
fore, the  rate  of  hydration  of  sodium  pyrophosphate  is  not  a 
direct  function  of  the  pyrophosphate  concentration  nor  of  the 
hydrogen  ion  concentration,  due  to  the  three  influences  that 
hydrogen  ion  must  have  in  the  hydration ; — first  of  repres- 
sion of  the  pyrophosphoric  acid  ionization,  second  of  re- 
pression of  the  orthophosphoric  acid  ionization,  and  third, 
and  by  far  the  greatest,  that  of  increasing  the  rate  of  the 
hydration. 


The  curves  appearing  in  this  article  were  prepared  from 
tracing  made  by  Mr.  S.  J.  Ballard,  draftsman,  of  the  Depart- 
ment of  Chemical  Engineering. 

SUMMARY 

I.  Three  concentrations   of   Normal   Sodium   Pyrophos- 
phate each  in  three  different  concentrations  of  hydrochloric 
acid,  making  nine  solutions  of  different  hydrogen  ion  concen- 
tration were  studied. 

II.  By  use  of  analytical  curves  obtained  by  making  up 
synthetic  solutions  and  plotting  molar  concentration  of  hy- 
drogen ion  against  molar  concentration  of  di-sodium  ortho- 
phosphate,   each  hydration  was   followed   to  completion   by 
hydrogen  ion  concentration  measurements. 

III.  The  last  fifty  per  cent,  of  each  hydration  was  checked 
by   the   standard   gravimetric   method.     The    separation    of 

46 


ortho-  and  pyrophosphate  was  made  by  use  of  a  magnesium 
chloride  mixture. 

IV.  The   hydrogen    ion    concentration   in    each    solution 
decreased  progressively  with  time  reaching  a  final  constant 
value. 

V.  The   times   required   for   equilibrium   within    experi- 
mental error  for  a  .125  M.  Na4P2O7  solution  with  .500  M., 
.425  M.,  and  .350  M.  HC1  were  250  hours,  702  hours,  and  1,302 
hours  respectively;    for  a  .175  M.  Na4P.,O7  solution  with  .500 
M.,  .425  M.,  and  .350  M.  HC1  the  times  for  equilibrium  were 
1,160  hours,  1,493  hours  ,and  2,386  hours  respectively;    and 
for  a  .225  M.  Na4P,O7  solution  with  .500  M.  and  .425  M.  HC1 
the  times  for  equilibrium]  were  1,688  hours  and  2,719  hours 
respectively.     2,766  hours  were  required  for  81%   hydration 
of  a  .225  M  Na.P.O,  solution  with  .350  M.  HC1.     It  would 
require  at  a  minimum  three  months  longer  for  completion  if  it 
continued  at  the  same  rate  as  it  was  going  over  the  last  twenty 
per  cent. 

VI.  The  influence  of  hydrogen  ion  cannot  be  accounted 
for  by  its  effect  upon  the  ionic  equilibrium  of  the  pyrophos- 
phoric  and  orthophosphoric  acid  alone. 


47 


REFERENCES 

1  Graham,  Phil,  Trans.,  123,  53,  1833. 

2  Sabatier,  Compt.  Rendu.,  106,  63,  1888. 

8  Montemartini  and  Egid,  Gass.  Ital.  Chim.,  31  I,  394,  1901. 

4Balarefr,  Zeit.  Anorg.  Chem.,  67,  234,  1909;   68,  288,  1901; 
96,  103,  1916. 

5Berthelot  and  Andre,  Compt.  Rendu.,  123,  776,  1896;    124, 
265,  1897;   124,261,  1897. 

c  Giran,  J.  Russ.  Chem.  Soc.,  30,  99. 

7  Holt  and  Meyers,  J.  C.  S.  Trans.,  99,  385,  1911. 

8  Beans  and  Kiehl,  Unpublished  work.  (Submitted  as  Disser- 

tation by  Kiehl,  1921). 

9  Abbott,  J.  A.  C.  S.,  31,  763,  1909. 

10  Fales  and  Vosburg,  J.  A.  C.  S.,  40,  1291,  1918. 

11  Ellis,  J.  A.  C.  S.,  38,  737,  1916. 
12Hulett,  Zeit,  Physik.  Chem.,  33,  611,  1920. 
18  Fales  and  Mudge,  J.  A.  C.  S.,  42,  2434,  1920. 
14  Arnold  and  Werner,  Chem.  Zeit.,  29,  1905. 


VITA 

Waldemar  C.  Hansen  was  born  in  Meade  County,  South 
Dakota,  February  9,  1896.  He  was  graduated  from  Montana 
State  College  in  June,  1917.  He  served  from  October,  1917 
to  March,  1919,  with  The  First  Gas  Regiment  United  States 
Army,  A.  E.  F.  During  the  summer  of  1919  he  was  Food 
and  Drug  Inspector  for  the  Montana  State  Board  of  Health, 
Helena,  Montana.  He  was  a  graduate  student  and  an  assist- 
ant in  the  Department  of  Chemistry  of  the  State  University 
of  Iowa  ,Iowa  City,  Iowa,  during  the  year  1919-20  and  sum- 
mer of  1920.  He  was  a  graduate  student  in  the  Department 
of  Chemistry  of  Columbia  University  during  the  years 
1920-21,  1921-22,  and  summer  of  1921.  He  was  a  laboratory 
assistant  during  the  years  1920-21  and  1921-22,  and  an  as- 
sistant in  the  Department  of  Chemistry  in  Columbia  Univer- 
sity from  February  1  to  July  1,  1922. 


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